Single-Slit Diffraction (HL) (HL IB Physics)

• The intensity pattern of light can be represented as a series of light and dark fringes which show the areas of maximum and minimum intensity
• If a laser emitting blue light is directed at a single slit, where the slit width is larger than the wavelength of the light, it will spread out as follows:

The intensity pattern of blue laser light diffracted through a single slit

• The features of the single slit diffraction pattern are:
  • A central maximum with a high intensity
  • Subsidiary maxima equally spaced, successively smaller in intensity and half the width of the central maximum

• The width of the central maximum changes depending on the wavelength of the light
• This is calculated by the equation:

• Where:
  • θ = angle between the central maximum and first minimum (°)
  • λ = wavelength of incoming light (m)
  • b = width of the single slit (m)

Single-slit diffraction

• The angle θ tells us how spread out the diffraction pattern is 
• This equation shows us that the pattern is more spread out if:
  
  • The width of the slit is reduced
  • The wavelength of the incoming light is increased

• This can also be compared to distances
• Since θ is a very small angle, we can approximate it to:

• Where:
  • y = distance between the central maximum and first minimum (m)
  • d = distance between single-slit and screen (m)

Single slit diffraction in terms of distances

Different Wavelengths of Light

• The angle of diffraction, θ is directly proportional to the wavelength of the light, λ
  • This means that the width of the bright maxima, or fringe, is also proportional to the wavelength

• Red light – which has the longest wavelength of visible light – will produce a diffraction pattern with wide fringes
• Blue light – which has a much shorter wavelength – will produce a diffraction pattern with narrow fringes

Fringe width depends on the wavelength of the light

• Therefore, if the blue laser were to be replaced with a red laser:
  • The wavelength of red light is longer so the light would diffract more
  • The intensity fringes would therefore be wider

The intensity pattern of red laser light shows longer wavelengths diffract more than shorter blue wavelengths

• If the slit was made narrower:
  • The intensity would decrease
  • The fringe spacing would be wider

Spectrum for White Light

• If the laser were to be replaced by a non-laser source emitting white light:
  • The central maximum would be white
  • All maxima would be composed of a spectrum
  • The shortest wavelength (violet / blue) would appear nearest to the central maximum
  • The longest wavelength (red) would appear furthest from the central maximum
  • The colours look blurry and further away from the central maxima the fringe spacing gets so small that the spectra eventually merge without any space between them
  • As the maxima move further away from the central maximum the wavelengths of blue colour observed decrease and the wavelengths of red observed increase
  • The fringe spacing would be smaller and the non-central maxima would be wider

Qualitative treatment of the variation of the width of the central diffraction maximum with wavelength and slit width

• When light is passed through both a single slit, then a double slit, the resultant pattern is one in which the single-slit pattern modulates the double-slit pattern

 

Light travelling through both a single then double slit

• The slit-slit interference pattern has a distinctive central maxima, and subsequent minima at lower intensity
• The double-slit interference pattern has equally spaced lines at equal maxima
• Together, the combined pattern has equally spaced lines but now in a single slit 'envelope' 

A modulated double-slit interference pattern

• The pattern now decreases in intensity the further it is from the centre